Backbone Dynamics of the Monomeric λ Repressor Denatured State Ensemble under Nondenaturing Conditions

Abstract

Oxidizing two native methionine residues predominantly populates the denatured state of monomeric λ repressor (MetO-λ_LS) under nondenaturing conditions. NMR was used to characterize the secondary structure and dynamics of MetO-λ_LS in standard phosphate buffer. ¹³C_α and ¹H_α chemical shift indices reveal a region of significant helicity between residues 9 and 29. This helical content is further supported by the observation of medium-range amide NOEs. The remaining residues do not exhibit significant helicity as determined by NMR. We determined ¹⁵N relaxation parameters for 64 of 85 residues at 600 and 800 MHz. There are two distinct regions of reduced flexibility, residues 8–32 in the N-terminal third and residues 50–83 in the C-terminal third. The middle third, residues 33–50, has greater flexibility. We have analyzed the amplitude of the backbone motions in terms of the physical properties of the amino acids and conclude that conformational restriction of the backbone MetO-λ_LS is due to nascent helix formation in the region corresponding to native helix 1. The bulkiness of amino acid residues in the C-terminal third leads to the potential for hydrophobic interactions, which is suggested by chemical exchange detected by the difference in spectral density J(0) at the two static magnetic fields. The more flexible middle region is the result of a predominance of small side chains in this region.

Protein folding, while an essential process in biology, is not well-understood in detail. It is known, however, that the nature of the denatured state is a critical aspect in the mechanism of protein folding, because it affects the thermodynamics and kinetics of folding (1). Since most natural proteins are stable, to study the denatured state, it is necessary to find a way to populate it. The most relevant denatured state model would be one that exists under physiological conditions that favor the native state because this denatured state is the starting point for folding.

To understand the forces that drive the folding of monomeric λ repressor, we developed a model of the denatured state under nondenaturing conditions by oxidizing its two methionines. We call our model MetO-λ_LS¹ (2). The circular dichroism spectrum of the predominantly unfolded MetO-λ_LS indicates that it possesses significant helicity under native-like conditions, but circular dichroism provides information about only the average secondary structure of all residues. To determine whether specific regions of the molecule are more likely to be helical than others, it is necessary to use a technique that provides residue-specific information, such as NMR.

NMR relaxation experiments can quantify the flexibility of a protein on a residue-by-residue basis. ¹⁵N backbone dynamics have been used to study the denatured states of staphylococcal nuclease (3), the SH3 domain of drk (4), the D2 domain of annexin I (5), apomyoglobin (6), fibronectin type III (7), reduced hen lysozyme (8), and protein G (9). The dynamics of the most highly denatured of these proteins, protein G and the fibronectin type III domain, are relatively uniform over the entire molecule, indicating a high degree of flexibility. The proteins studied under more native-like conditions, staphylococcal nuclease, apomyoglobin, and the D2 domain of annexin I, exhibit more variability in the relaxation parameters and have regions of reduced flexibility. The interpretation of these results is varied. One group correlates the reduced flexibility with secondary structure (5), while another hypothesizes that rigidity is due to hydrophobic interactions (10). A third group combines these ideas by hypothesizing that secondary structure formation is the result of hydrophobic interactions (11). In summary, there is not yet a good molecular explanation for regions of reduced flexibility in denatured proteins.

In this study, we used NMR to characterize the structural and dynamic properties of the MetO-λ_LS form of monomeric λ repressor under nondenaturing conditions. We first assigned the backbone resonances and then used these data, in combination with other NMR experiments, to assess the structural properties and backbone dynamics of this denatured state model.

EXPERIMENTAL PROCEDURES

Overexpression and Protein Purification

The variant of monomeric λ repressor used in this study, λ_LS, consists of residues 1–85 with the following substitutions: G46A, G48A, I54K, I56K, and S77A. λ_LS was overexpressed in BL21(DE3) cells (Stratagene) from the gene under the T7 promoter in the pET9a vector from Novagen. For ¹⁵N-labeled protein, the bacteria were grown in M9 minimal medium (6 g/L Na₂HPO₄, 3 g/L KH₂PO₄, 0.5 g/L NaCl, 1 mM MgSO₄, 0.1 mM CaCl₂, and 2 g/L glucose) supplemented with 1 g/L ¹⁵NH₄Cl either with or without 1% ¹⁵N BioExpress from Cambridge Isotope Labs. For ¹⁵N- and ¹³C-labeled protein, the bacteria were grown in M9 minimal medium (6 g/L Na₂HPO₄, 3 g/L KH₂PO₄, 0.5 g/L NaCl, 1 mM MgSO₄, and 0.1 mM CaCl₂) supplemented with 1 g/L ¹⁵NH₄-Cl and 2 g/L [¹³C]glucose from Cambridge Isotope Labs. Expression was induced at an OD of 0.4–0.6 by addition of IPTG to a concentration of 0.4 mM. The cells were incubated at 37 °C for a further 3–4 h before being harvested by centrifugation and resuspended in lysis buffer [50 mM Tris-HCl and 10 mM EDTA (pH 8.0)].

λ_1–85 variants were purified by a modified version of an earlier protocol (12). Cell lysates were generated in a French pressure cell at 12 000 lb/in.² The lysates were run through a DEAE Sephacel column (Amersham Biosciences) to remove cell debris and other proteins. The flow-through was collected and applied directly to an Affigel Blue (Bio-Rad) column that was run in phosphate buffer at pH 7. The protein was eluted from the column in 300 mM KCl. The eluted fraction was dialyzed against degassed distilled H₂O overnight and then lyophilized. (Degassed water was used to minimize methionine oxidation during purification.) The lyophilized protein was redissolved in deionized H₂O and further purified by size-exclusion chromatography on a Sephadex G-50 column (Amersham Biosciences). The final purity of each protein was checked by reverse-phase HPLC and electrospray mass spectrometry. For each protein, the MS-determined mass was within 1 amu of the expected mass, further confirming the proper amino acid substitutions. Both HPLC and mass spectrometry indicated no significant oxidation of the methionine residues. All protein concentrations were determined using the method of Edelhoch (13).

Protein Oxidation

Methionine oxidation was carried out as follows. Lyophilized protein was hydrated in deionized water to a concentration of 1 mg/mL. To the protein solution were added ~20 µL of 0.1 M perchloric acid per milliliter to bring the pH below 3 and 30% hydrogen peroxide to a final concentration of 0.05%. This solution was incubated on the bench for 45 min before a spin column was used for buffer exchange into the sample buffer [20 mM phosphate and 100 mM NaCl (pH 6)]. Oxidation of methionine to sulfoxide was checked by reverse-phase HPLC and electrospray mass spectrometry.

NMR Spectroscopy

All three-dimensional NMR spectra were recorded at 25 °C on a Varian Unity 800 spectrometer with a triple-resonance z-shielded gradient cryoprobe on samples at concentrations of 0.2–0.4 mM in 20 mM sodium phosphate buffer (pH 6). Two-dimensional gradient-enhanced sensitivity-enhanced ¹H–¹⁵N HSQC experiments (14) were conducted with a spectral width in the ¹H dimension of 7000 Hz and 1024 complex points and a spectral width in the ¹⁵N dimension of 1500 Hz and 128 complex points. Denatured state resonance assignments were made by using a suite of triple-resonance experiments, including HNCO (15), (HCA)CO(CA)NH (16), HNCACB (17), and HN(CO)-CACB (18). In all of the three-dimensional NMR spectra of the native state, the spectral width in the ¹H dimension was 8000 Hz with 1024 complex points. The spectral width in the ¹⁵N dimension was 1500 Hz with 34 or 37 complex points. The spectral width in the ¹³C dimension was 3000 Hz with 40 complex points for the HNCO experiments. The spectral width was 10 000 Hz with 70 complex points for the HNCACB and HN(CO)CACB experiments. All NMR spectra were processed using NMRPipe (19). Three-dimensional spectra were analyzed using NMRView (20) or CARA (21) (CARA can be downloaded free from www.nmr.ch).

NOESY-HSQC

NOESY spectroscopy of MetO-λ_LS was performed using a 200 ms mixing time. This mixing time is long compared to the times used for native proteins. The danger in using long mixing times in native proteins is that there may be signals from spin diffusion rather than real NOEs. Spin diffusion is not a large problem in denatured proteins, which allows for the use of longer mixing times to obtain more intense NOEs (22).

Relaxation Measurements

All NMR spin relaxation measurements were performed on a single sample at a protein concentration of 0.2 mM in 20 mM sodium phosphate buffer at pH 6.0 with 10% ²H₂O. The data were obtained using proton-detected, sensitivity- and gradient-enhanced inversion-recovery and CPMG pulse sequences for R₁ and R₂, respectively (23), on Varian INOVA 600 MHz and Varian INOVA 800 MHz instruments at the Duke University NMR Center. Spectra at 600 MHz were collected as 1024 × 64 complex points with 32 transients and spectral widths of 8000 and 1350 Hz in the ¹H and ¹⁵N dimensions, respectively. Spectra at 800 MHz were collected as 1024 × 64 complex points with 32 transients and spectral widths of 10 000 and 1800 Hz in the ¹H and ¹⁵N dimensions, respectively. The longitudinal relaxation rates, R₁, were determined using inversion–recovery delays of 10, 40, 80, 100, 150, 230, 430, 630, and 840 ms at 600 and 800 MHz. The transverse relaxation rates, R₂, were determined with CPMG delays of 10, 30, 50, 70, 90, 110, 150, and 170 ms at 600 MHz and 10, 30, 50, 70, 90, 110, 130, and 150 ms at 800 MHz. {¹H}−¹⁵N heteronuclear NOEs were determined using spectra collected with a 3 s saturation period and a 2 s recycle delay or no saturation and a 5 s recycle delay at 600 and 800 MHz. Spectra were processed using NMRPipe; peak intensities were determined using Sparky (T. D. Goddard and D. G. Kneller, SPARKY 3, University of California, San Francisco), and relaxation rates were determined by a fitting to a two-parameter single-exponential decay equation. Errors in relaxation parameters are from the fits by Sparky.

Reduced Spectral Density Function Mapping

The measured relaxation parameters are related to the spectral density function of the amide bond vector by the following equations (24):

$$\frac{1}{T_1}=\frac{d^2}{4}[J({\omega }_{\mathrm{H}}-{\omega }_{\mathrm{N}})+3J({\omega }_{\mathrm{N}})+6J({\omega }_{\mathrm{H}}+{\omega }_{\mathrm{N}})]+c^{2}J({\omega }_{\mathrm{N}})$$ (1)

$$\frac{1}{T_2}=\frac{d^2}{8}[4J(0)+J({\omega }_{\mathrm{H}}-{\omega }_{\mathrm{N}})+3J({\omega }_{\mathrm{N}})+6J({\omega }_{\mathrm{H}}+{\omega }_{\mathrm{N}})]+\frac{c^2}{6}[3J({\omega }_{\mathrm{N}})+4J(0)]$$ (2)

$$\text{NOE}=1+\left(\frac{d^2}{4}\right)\left(\frac{{\gamma }_{\mathrm{H}}}{{\gamma }_{\mathrm{N}}}\right)[6J({\omega }_{\mathrm{H}}+{\omega }_{\mathrm{N}})-J({\omega }_{\mathrm{H}}-{\omega }_{\mathrm{N}})]T_1$$ (3)

where d = (µ₀hγ_Hγ_N)/(8π²r_NH³), $c=({\gamma }_{\mathrm{N}}{B}_0\mathrm{\Delta }\sigma )/\sqrt{3}$, ω_H and ω_N are the Larmor frequencies of the ¹H and ¹⁵N nuclei, respectively, µ₀ is the permeability of free space, γ_H and γ_N are the gyromagnetic ratios of ¹H and ¹⁵N, respectively, h is Planck’s constant, Δσ is the chemical shift tensor, and r_NH is the length of the amide bond vector. The values used for Δσ and r_NH are −170 ppm and 1.02 Å, respectively.

The relaxation parameters were analyzed using reduced spectral density function mapping to determine spectral density values at three frequencies (25). Assuming that J(ω) is effectively constant when ω ≈ ω_H on the basis of Method 1 of Farrow et al. (25), eqs 1–3 are modified so that J(ω_H), J(ω_H – ω_N), and J(ω_H + ω_N) are replaced by J(0.87ω_H) and rewritten as follows:

$$\frac{1}{T_1}=\frac{d^2}{4}[3J({\omega }_{\mathrm{N}})+7J(0.87{\omega }_{\mathrm{H}})]+c^{2}J({\omega }_{\mathrm{N}})$$ (4)

$$\frac{1}{T_2}=\frac{d^2}{8}[4J(0)+3J({\omega }_{\mathrm{N}})+13J(0.87{\omega }_{\mathrm{H}})]+\frac{c^2}{6}[3J({\omega }_{\mathrm{N}})+4J(0)]$$ (5)

$$\text{NOE}=1+\left(\frac{d^2}{4}\right)\left(\frac{{\gamma }_{\mathrm{H}}}{{\gamma }_{\mathrm{N}}}\right)[5J(0.87{\omega }_{\mathrm{H}})]T_1$$ (6)

These equations relate the observed relaxation parameters to the spectral density function at three frequencies based on the following equations:

$$J(0.87{\omega }_{\mathrm{H}})=R_1(\text{NOE}-1)\frac{{\gamma }_{\mathrm{N}}}{{\gamma }_{\mathrm{H}}}\frac{4}{5d^2}$$ (7)

$$J({\omega }_{\mathrm{N}})=\frac{R_1-J(0.87{\omega }_{\mathrm{H}})(7d^2/4)}{(3d^2/4)+c^2}$$ (8)

$$J(0)=\frac{R_2-J({\omega }_{\mathrm{N}})(3d^2/8+c^2/2)-J(0.87{\omega }_{\mathrm{H}})(13d^2/8)}{d^2/2+2c^2/3}$$ (9)

where R₁ = 1/T₁ and R₂ = 1/T₂.

The value of J(0.87ω_H) was calculated using eq 7 and the values of NOE and T₁. Values of J(ω_N) and J(0) were calculated using eqs 8 and 9, repectively.

Lipari—Szabo Model-Free Analysis

The original model-free formalism from Lipari and Szabo (26, 27) was used to determine τ_e and S² using the relxn2.2 program (28) written by A. Lee according to the following equation:

$$J(\omega )=\frac{2}{5}[\frac{S^2{\tau }_{\mathrm{m}}}{1+{(\omega {\tau }_{\mathrm{m}})}^2}+\frac{(1-S^2)\tau }{1+{(\omega \tau )}^2}]$$ (10)

where 1/τ = 1/τ_m + 1/τ_e, τ_m is the global correlation time, and τ_e is a fast internal motion time. The values used for Δσ and r_NH are −170 ppm and 1.02 Å, respectively.

Physical and Chemical Parameters of Primary Structure

The per-residue AABUF and bulkiness using the values of Rose et al. (29) and Zimmerman et al. (30) were calculated utilizing the Expasy website, with a seven-residue moving-average window.

RESULTS

Backbone Assignments

Standard multidimensional NMR experiments were used to assign the backbone atoms of MetO-λ_LS under native conditions. These experiments included HNCO, HNCACB, and HN(CO)CACB. The experiments detecting ¹³C_α and ¹³C_β were used to make some sequential assignments. Unfortunately, the chemical shift degeneracy of the C_α and C_β nuclei and the repeats in the sequence make it difficult to distinguish between residues of the same type. To overcome this problem, we exploited the chemical shift dispersion in the ¹³CO atom by using the (HCA)CO(CA)NH experiment (16). In combination with the HNCO experiment, this pulse sequence allows sequential assignments to be made through the ¹³CO atoms. We obtained sequential assignments for 73 of 83 non-proline residues in MetO-λ_LS. The assigned ¹H–¹⁵N HSQC spectrum of MetO-λ_LS is shown in Figure 1. The chemical shifts for the backbone nuclei in MetO-λ_LS are listed in the Supporting Information.

Figure 1.

¹H–¹⁵N HSQC spectrum (800 MHz) of MetO-λ_LS in 20 mM phosphate buffer at pH 6 and 25 °C.

Deviation from Random Coil Chemical Shifts

Chemical shift indices provide an indication of nascent helicity in the denatured state. There are four nuclei that can be used for chemical shift deviation calculations: ¹³C_α, ¹³C_β, ¹³CO, and ¹H_α (31). A systematic study of the correlation between chemical shift index and secondary structure shows that the best statistical correlation is provided by the random coil values of Schwarzinger et al. (32). Shown in Figure 2 are the chemical shift index values versus residue number for ¹³C_α and ¹H_α atoms in MetO-λ_LS determined using sequence-corrected random coil values from Schwarzinger et al. (33).

Figure 2.

Difference between chemical shifts for (A) ¹³C_α and (B) ¹H_α in MetO-λ_LS and sequence-corrected random coil chemical shifts from Schwarzinger et al. (33). The bars indicate the position of helices in the native state.

Short-Range and Medium-Range Amide NOEs from NOE-SY-HSQC

In general, there are fewer NOEs detected in denatured proteins than in native globular proteins. Forty-four assignable short-range and medium-range amide NOEs are detected in MetO-λ_LS using a three-dimensional NOESY-HSQC experiment. None of these NOEs are from amide ¹H resonances more than five residues apart. A summary of the medium-range NOEs is shown in Table 1, and the short-range NOEs are shown in Figure 3.

Table 1.

Medium-Range H_N–H_N NOEs from Three-Dimensional NOESY-HSQC Spectra

atom 1	atom 2	range	atom 1	atom 2	range
Gln 11	Thr 8	3	Val 73	Ile 68	5
Lys 26	Tyr 22	4	Ile 68	Ser 72	4
Leu 31	Asn 27	4	Ile 80	Ala 77	3
Phe 51	Val 47	4	Ile 84	Ile 80	4
Lys 67	Leu 64	3

Figure 3.

Short-range H_N–H_N and H_N–H_α NOEs in MetO-λ_LS observed in a NOESY-HSQ spectrum obtained with a mixing time of 200 ms.

Typically, two kinds of short-range NOEs identify secondary structure in denatured proteins. The d_NN(i, i + 1) NOEs are more prevalent in helical conformations. The d_Nα(i, i + 1) NOEs are more prevalent in extended conformations (34). The slightly longer-range d_NN(i, i + 2) NOEs are commonly found in α- and 3₁₀-helices (34). Although the total number of NOEs is small for MetO-λ_LS, there are several indicative of helical structure in the region corresponding to helix 1 in the native state. There are many d_NN(i, i + 1) and d_NN(i, i + 2) NOEs in the region between residues 8 and 33. A few medium-range NOEs are clustered in regions corresponding to helices 1, 4, and 5 in the native state. However, only the region corresponding to helix 1 exhibits a consistent stretch of short-range NOEs.

¹⁵N Relaxation

The ¹⁵N relaxation parameters, R₁, R₂, and heteronuclear NOE ({¹H}−¹⁵N NOE), were quantified for 64 of 85 residues in MetO-λ_LS at static magnetic fields of 600 and 800 MHz. The other residues either are prolines, are unassigned, or have intensities too low to obtain reasonable fits. These relaxation data are shown in Figure 4. A table of these values is provided in the Supporting Information.

Figure 4.

Relaxation parameters from 600 (●) and 800 MHz (○) vs residue number for MetO-λ_LS in 20 mM phosphate buffer at pH 6 and 25 °C: (A) ¹⁵N longitudinal relaxation rate, R₁, (B) ¹⁵N transverse relaxation rate, R₂, and (C) heteronuclear NOEs with a proton saturation period of 3 s.

R₁ is relatively uniform across the sequence of the protein, except for small decreases at the N- and C-termini. There is more variation of R₂ over the sequence. The R₂ is small, around 3–4 s⁻¹ at 600 MHz, at the termini and between residues 32 and 48. Above average values are observed between residues 8–32 and 50–82. Most of the {¹H}−¹⁵N NOE values are less than 0.5, which is typical of denatured proteins. The pattern of the {¹H}−¹⁵N NOEs follows that of R₂, with the lowest values at the termini, a low region in the middle, and two regions of above average values. Although R₁ and heteronuclear NOEs are both sensitive to high-frequency motions, it appears that R₁ is less sensitive because the R₁ values are not low in the middle of the molecule where the heteronuclear NOEs are low.

The values of R₂ can be increased by conformational exchange due to self-association (35). The R₂ value at 600 MHz was estimated for five protein concentrations ranging from 0.05 to 0.4 mM in determining the contribution to R₂ from self-association. For most residues, the contribution to R₂ from R_ex is less than 1 s⁻¹ at a protein concentration of 0.2 mM, which is within error. For the residues whose R₂ values are most sensitive to self-association, the maximum amount of R_ex from this source is 2.7 s⁻¹ at a protein concentration of 0.2 mM.

Spectral Density Mapping

Spectral density mapping, developed by several groups, allows a description of the spectral density function to be generated using ¹⁵N relaxation data (36–38). The reduced spectral density mapping method formulated by Farrow et al. uses R₁, R₂, and NOE values to calculate values of the spectral density at three frequencies: J(0), J(ω_N), and J(0.87ω_H) for each static magnetic field (see Experimental Procedures) (25). Using this approach and data collected at two static magnetic fields, we calculated values of the spectral density for 64 residues at five frequencies: 0, 60, 80, 522, and 696 MHz. Histograms of the spectral densities at J(0), J(ω_N), and J(ω_0.87H) are shown in Figure 5.

Figure 5.

Calculated values of the spectral density function at J(ω_0.87H), J(ω_N), and J(0) for MetO-λ_LS from relaxation data at 600 (●) and 800 MHz (○) corresponding to J(696), J(522), J(80), J(60), and J(0).

There is little variation in J(ω_N), except at the termini where the values are diminished, which is shown in Figure 5B. J(0.87ω_H) exhibits more variation with larger values at the termini and in the middle of the molecule, which is shown in Figure 5A. The relative increase in fast motions (~200 ps) indicated by larger values of J(0.87ω_H) at the termini is typical of native and denatured proteins. In the middle of the protein, there is an increase in the contribution of fast motions to the spectral density function (panel A) without a concomitant decrease in the contribution of intermediate timescale motions (panel B).

The spectral density at zero frequency, J(0), applies to motions equal to and slower than the global correlation time, τ_c. The value of J(0) is the only spectral density for which there is a contribution from R₂. Motions slower than the correlation time increase the value of R₂ by contributing to chemical exchange (R_ex). This elevation in R₂ will lead to an artifactual increase in J(0). The values of J(0) calculated from relaxation data at 600 and 800 MHz are shown in Figure 5C. J(0) is smaller at the termini and in the middle of the protein due to the increase in the magnitude of faster motions in these regions indicated by the increases in J(0.87ω_H). The higher values of J(0) indicate the regions where there is reduced flexibility in MetO-λ_LS. For some residues, the value of J(0) is larger at 800 MHz than at 600 MHz. This increase is probably due to contributions from chemical exchange. The contribution to relaxation (R_ex) is discussed further in the next section.

Model-Free Analysis

While reduced spectral density mapping allows probabilities of motions at particular time scales to be determined, it does not provide a molecular interpretation of those motions. The original model-free formalism developed by Lipari and Szabo assumes that the molecule undergoes slow isotropic tumbling at the global correlation time with faster, spatially restricted internal motions at a time τ_e (26, 27). The order parameter, S², describes the fraction of motion that can be attributed to isotropic tumbling and ranges between 0 and 1, where 1 represents a totally rigid N–H bond.

A global correlation time is required to apply the standard model-free analysis to relaxation data. However, the tumbling of a partially folded or unfolded molecule may not be described well by a single correlation time (3). One solution that we applied to this problem is to treat each residue as a separate dynamic segment and to fit a separate correlation time to each residue (3). The parameters determined using the model-free equations to fit for S², τ_e, and a τ_m for each residue are shown in Figure 6. The average τ_m determined by this method is 6.7 ns with a standard deviation of 2.7 ns. This model has an average χ² normalized for the number of parameters that is lower than those of other models discussed below and therefore seems to be the best model describing the relaxation of most residues in MetO-λ_LS. However, six residues (47, 51, 59, 72, 74, and 81) have anomalously high τ_m values which are better fit to a model that includes R_ex as a fitting parameter.

Figure 6.

Model-free parameters for MetO-λ_LS derived from ¹⁵N relaxation measurements at 600 and 800 MHz using the model fitting S², τ_e, and τ_m.

The model in which S², τ_e, and a τ_m were fitted did not provide information about the contribution to relaxation from chemical exchange. To apply the standard model-free analysis to relaxation data for MetO-λ_LS, and obtain values for R_ex, an estimate for the global correlation time was required. A τ_m can be fit using a global model-free fit to all the relaxation data, which accounts for the effect of fast internal motions (39). This method yielded a τ_m value of 6.9 ns. Anisotropic motion could distort the value of τ_m determined by this method (28); however, it is likely that conformational averaging in MetO-λ_LS leads to isotropic tumbling (3). In a similar approach, Tjandra and Bax removed residues with internal motions that led to low NOEs (40). A NOE cutoff of 0.6, which includes only residues 9, 11–21, and 84, also gave a τ_m value of 6.9 ns. This value is well within experimental error of the average obtained from the individual τ_m values obtained from the fit described above.

The correlation time of a native globular protein is often determined by using the ratio of T₁ to T₂ values (41). Using this procedure, the τ_m is 5.3 ns from the 800 MHz data and 5.0 ns from the 600 MHz data. This method does not account for internal motions that affect the values of T₁ and T₂ (28). The τ_m value from the T₁/T₂ ratio is probably an underestimate because it ignores fast internal motions in the protein and the most reasonable correlation time is the one from global fitting of the relaxation parameters to the model-free equations.

In summary, we used a global correlation time, τ_m, of 6.9 ns to fit the relaxation data from both static magnetic fields to two additional models that include R_ex: (1) S² and R_ex and (2) S², τ_e, and R_ex. Of the two models, the χ² for the model fitting three parameters, S², τ_e, and R_ex, was the lowest. These model-free parameters versus residue number are shown in Figure 7. The majority of the order parameters are below 0.8, which is consistent with a denatured protein. The pattern of order parameters is the same for both the model that fits a τ_m for each residue and the model that uses a global correlation time. The pattern supports the conclusions from reduced spectral density mapping. Both types of analyses show two regions of reduced flexibility, between residues 8 and 31 and between residues 50 and 82, with increased flexibility at the termini, and between residues 32 and 49.

Figure 7.

Model-free parameters for MetO-λ_LS derived from ¹⁵N relaxation measurements at 600 and 800 MHz using the model fitting S², τ_e, and R_ex.

Lipari—Szabo Mapping

Analysis of spectral density functions without the need to fit model-free parameters is accomplished using the graphical Lipari–Szabo mapping developed by Andrec et al. (42). In this analysis, J(ω_0.87H) versus J(ω_N) is plotted for each residue. A theoretical curve for rigid tumbling is shown as a line with correlation times indicated. The relative distance between a residue and the point for rigid tumbling is indicative of the order parameter, S². This analysis, shown in Figure 8, supports the finding that the middle of the molecule is much more flexible than the regions between residues 8–32 and 50–82 because residues 33–49, which are colored green, are farther from the rigid tumbling line at 6.9 ns. The three types of analysis used for the relaxation data, reduced spectral density mapping, model-free analysis, and Lipari–Szabo mapping, all indicate that the residues in the middle third of MetO-λ_LS are the most flexible with reduced flexibility in the N-terminal and C-terminal thirds.

Figure 8.

Lipari-Szabo maps for the analysis of MetO-λ_LS backbone dynamics using the method described by Andrec et al. (42) at (A) 600 and (B) 800 MHz. The points on the maps correspond to residues in the protein and have been colored according to their position in the primary structure, shown in the legend.

DISCUSSION

Backbone Flexibility Correlates with Amino Acid Composition

The amplitudes of the order parameters from Lipari–Szabo model-free analysis correlate surprisingly well with the size of the amino acids in MetO-λ_LS. Side chain bulkiness, defined by Zimmerman et al. as the ratio of the side chain volume to length, is plotted versus residue number in Figure 9A (30). The order parameter correlates with this property with a correlation coefficient of 0.52 and a p value of 1.9 × 10⁻⁵, shown in Figure 9B. There is a precedent for correlation of motional parameters in denatured proteins with physical properties of amino acids. A parameter called “average area buried upon folding” (AABUF) developed by Rose et al. (29) correlates well with dynamic properties in the denatured state of apomyoglobin at pH 2.3 (10). This correlation persists even when apomyoglobin is denatured in 8 M urea at pH 2.3 (43). The authors concluded that local hydrophobic interactions persist even in 8 M urea because the regions of rigidity correspond to regions where AABUF is high. The amplitudes of the order parameters in MetO- λ_LS also correlate well with AABUF (shown in Figure 9C), with a correlation coefficient of 0.56 and a p value of 3 × 10⁻⁶ (shown in Figure 9D).

Figure 9.

Physicochemical characteristics of the amino acid sequence of λ_LS calculated over a seven-residue moving average window: (A) bulkiness of the side chain (30) and (B) average area buried upon folding (29). Linear correlations between physicochemical characteristics of the amino acid sequence of λ_LS, (C) bulkiness (30) and (D) average area buried upon folding (29), and the order parameters of MetO-λ_LS from the model fitting S², τ_e, and R_ex.

Three Regions with Distinct Structural and Dynamic Properties

The source of the correlation between dynamic properties and the size of the side chain is different for three different regions in MetO-λ_LS. Chemical shift and NOE data indicate that the N-terminal region between residues 8 and 32 has significant nascent helicity and therefore has less backbone flexibility. The region in the middle of the protein between residues 33 and 50 is more flexible due to a predominance of small side chains leading to lower excluded volume restrictions on backbone motion. The C-terminal region between residues 50 and 83 is less flexible but does not seem to have significant secondary structure.

The chemical shifts and NOEs provide a consistent picture of regions of high helicity in this denatured ensemble. The chemical shift indices for ¹³C_α and ¹H_α lead us to conclude that residues in the helix 1 region of the native state have a distribution of ϕ and ψ values biased toward α-helical secondary structure in MetO-λ_LS. This conclusion is also consistent with the NOE data because the majority of the assigned NOEs are also observed in the same region. Additional evidence of nascent helical structure in helix 1 comes from previous studies of a peptide model of helix 1 of λ repressor, which exhibited 40% helicity by CD and demonstrated many d_NN(i, i + 1) and d_Nα(i, i + 3) NOEs that are indicative of helix formation (44). For the rest of the molecule, the lack of consistent stretches of helical chemical shifts and NOEs suggest that the backbone conformation is not strongly biased to the helical region of ϕ–ψ space.

The middle region of MetO-λ_LS, consisting of residues 33–50, exhibits a greater than average flexibility and consists of smaller amino acids. Regions with bulkier side chains are expected to have more steric hindrance, thereby limiting side chain flexibility more than smaller side chains. Regions of apomyoglobin at pH 2.3 with higher flexibility contain a number of Gly and Ala residues (43). The authors hypothesized that regions of polypeptides with small amino acids might act as “molecular hinges” that allow regions of nascent secondary structure to more easily come together (43).

The hinge in unfolded λ repressor near helix 3 may be an indirect consequence of the sequence requirements of protein function. Full-length bacteriophage λ repressor protein binds to DNA as a dimer and represses transcription. The helix–turn-helix motif that binds to DNA consists of helices 2 and 3. The residues that make the closest contact with the DNA are residues 45–50. In the wild-type sequence, this stretch of residues consists of one Ser, one Val, two Gly’s, one Ala, and one Leu. Since the N-terminal part of helix 3 fits furthest into the major groove of B-form operator DNA, small residues are required to make a good contact with the DNA (45). The presence of these small side chains leads to backbone flexibility in this region. Despite the fact that the variant used in the backbone dynamic studies of the denatured state has two Gly residues substituted with Ala in helix 3, it is still the region with the most flexibility.

Previous protein folding calculations using the diffusion-collision model have suggested that helices 1 and 4 form early in the folding pathway (46). The sequence of helix 4 is predicted by AGADIR (47) to have a high intrinsic helicity (in the absence of tertiary interactions) of 49%. However, there seems to be little nascent helicity in this region of MetO-λ_LS based on chemical shift indices and amide NOEs. The substitutions made in this variant are outside of this region so would not perturb the intrinsic helicity.

There are three types of evidence of conformational exchange in the C-terminal region of MetO-λ_LS. The difference between the J(0) spectral density function calculated at the two static magnetic fields for many residues in this region (bottom panel of Figure 5), higher-than-average order parameters, and according to one of the fitting models significant R_ex values (top panel of Figure 7) indicate conformational exchange. To contribute to R_ex, this conformational exchange must be relatively slow (micro- to milliseconds), suggesting that there is a barrier between two significantly populated (>5%) subensembles whose C-terminal conformations differ. This raises the question of the nature of the conformational exchange between these two subensembles. One possibility is a non-native hydrophobic collapse in this region, which has a number of hydrophobic residues. This might explain the lack of significant helical structure, despite the predicted high helical propensity of the sequence. Such a hydrophobic collapse might disfavor helix formation and is expected to be even greater in the wild-type protein, which has more hydrophobic resides (Ile and Ala) at positions 54 and 56 and unoxidized methionines (48).

Conformational Restriction Favors Protein Folding

The dynamics of proteins that are highly denatured, such as protein G in 7.4 M urea and the SH3 domain of drk in 2 M GdnCl, are relatively uniform over the entire molecule and indicate a high degree of flexibility. On the other hand, studies of proteins under more physiological conditions have shown that these polypeptides often contain regions of the molecule that are more rigid than others. These studies have interpreted the restricted flexibility as resulting from nascent helicity (5), hydrophobic interactions (10), or secondary structure formation due to hydrophobic interactions (11). Our results suggest that the sources of regions of conformational restriction in the denatured state of monomeric λ repressor populated under nondenaturing conditions are nascent helicity and a possible non-native hydrophobic interaction.

The size of conformational space for a denatured protein is critical to the our understanding of protein folding (49). The reduction of conformational space in unfolded proteins by restrictions imposed solely from steric hindrance and hydrogen bond satisfaction was found by Fitzkee and Rose to be 9 orders of magnitude (50). The addition of side chains would further restrict conformational space (51). Hence, conformational restriction seen in the backbone dynamics of unfolded proteins presumably comes from three sources: backbone sterics, solvation, and side chain sterics.

Protein folding is the result of a combination of opposing forces. Favorable forces include hydrogen bonding, electrostatics and van der Waals contacts in the protein, and the gain of entropy of the solvent. The main unfavorable force opposing folding is the loss of conformational entropy of the protein (52). In the native state, amino acid side chains are relatively restricted compared to the denatured state. The steric hindrance of bulky side chains leads to reduced flexibility and reduced backbone entropy. Even a small bias toward local structure, reflected in reduced backbone entropy, significantly reduces the conformational entropy of the denatured state. Therefore, the net loss of total entropy upon folding would decrease, making protein folding more favorable (53).

The evidence presented here suggests that, in the denatured state under native conditions, there is conformational restriction in the N- and C-terminal thirds of the monomeric λ repressor. In the N-terminal third, this restrictions lead to nativelike helix formation, which favors folding. In the C-terminal third, the NMR data suggest the absence of helicity despite an intrinsically helical sequence. This observation suggests that the conformational restriction in the region is due to non-native interactions. Whatever the source of conformational restriction, this too is expected to favor the native state by reducing the conformational entropy of the denatured state ensemble.